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On L 2 Solvability of BVPs for Elliptic Systems

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Abstract

In this article we prove solvability results for L 2 boundary value problems of some elliptic systems Lu=0 on the upper half-space \({\mathbb{R}} ^{n+1}_{+}, n\ge1\), with transversally independent coefficients. We use the first order formalism introduced by Auscher-Axelsson-McIntosh and further developed with a better understanding of the classes of solutions in the subsequent work of Auscher-Axelsson. The interesting fact is that we prove only half of the Rellich boundary inequality without knowing the other half.

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References

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Acknowledgements

Auscher thanks the Mathematical Science Institute of the Australian National University for hospitality and support where this work started. McIntosh acknowledges support from the Australian Government through the Australian Research Council. Mourgoglou was supported by the Fondation Mathématique Jacques Hadamard and thanks the University Paris-Sud for hospitality. We also thank Steve Hofmann and Andreas Rosén for discussions pertaining to this work.

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Authors and Affiliations

  1. Laboratoire de Mathématiques, UMR 8628 du CNRS, Univ. Paris-Sud, 91405, Orsay, France

    Pascal Auscher & Mihalis Mourgoglou

  2. Centre for Mathematics and its Applications, Mathematical Sciences Institute, Australian National University, Canberra, ACT, 0200, Australia

    Alan McIntosh

Authors
  1. Pascal Auscher
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  2. Alan McIntosh
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  3. Mihalis Mourgoglou
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Corresponding author

Correspondence to Pascal Auscher.

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Communicated by Yves Meyer.

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Auscher, P., McIntosh, A. & Mourgoglou, M. On L 2 Solvability of BVPs for Elliptic Systems. J Fourier Anal Appl 19, 478–494 (2013). https://doi.org/10.1007/s00041-013-9266-5

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  • DOI: https://doi.org/10.1007/s00041-013-9266-5

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